Solving Geometric Problems by Introducing an Equilateral triangle

Abstract

The article focuses on using an equilateral triangle as an auxiliary element in solving geometric (planimetric) problems. This method aims to simplify the problem-solving process and make it more intuitive by introducing an equilateral triangle in specific scenarios. By adding this triangle, the relationships between known and unknown quantities in the problem become more apparent or even obvious. The paper discusses four different scenarios where this method can be applied, illustrating each case with sample problems. The elegance and utility of the method in enhancing the solution process are highlighted. In this context, the applicability of this method in various olympiad problems or more complex geometric problems is demonstrated. This approach often reduces problems to simpler forms, saving time and effort in finding solutions. The paper provides evidence of the method’s effectiveness and offers guidance on its application.